Problem: Print all subsets of a set $S$, which contains $0, 1, ... n-1$ as elements. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements.

Constraints

* $1 \leq n \leq 18$

Input

The input is given in the following format.


$n$


Output

Print subsets ordered by their decimal integers. Print a subset in a line in the following format.


$d$: $e_0$ $e_1$ ...


Print ':' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Seprate two adjacency elements by a space character.

Example

Input

4


Output

0:
1: 0
2: 1
3: 0 1
4: 2
5: 0 2
6: 1 2
7: 0 1 2
8: 3
9: 0 3
10: 1 3
11: 0 1 3
12: 2 3
13: 0 2 3
14: 1 2 3
15: 0 1 2 3

Solution (in CPP):

Solution:
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <cctype>
#include <cassert>
#include <climits>
#include <string>
#include <bitset>
#include <cfloat>
#include <random>
#include <iomanip>
#include <unordered_set>
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int,int> > vpii;
typedef vector<pair<ll,ll> > vpll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vc> vvc;
typedef vector<vs> vvs;
typedef vector<vll> vvll;
typedef map<int,int> mii;
typedef set<int> si;
#define rep(i,n) for(ll i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define arep(i,v) for(auto i : v)
#define irep(it, stl) for(auto it = stl.begin(); it != stl.end(); it++)
#define drep(i,n) for(int i = (n) - 1; i >= 0; --i)
#define fin(ans) cout << (ans) << '\n'
#define STLL(s) strtoll(s.c_str(), NULL, 10)
#define mp(p,q) make_pair(p, q)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
#define MATHPI acos(-1)
#define fi first
#define se second
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
template <class T> inline bool chmax(T& a,T b){if(a<b){a=b;return 1;} return 0;}
template <class T> inline bool chmin(T& a,T b){if(a>b){a=b;return 1;} return 0;}
template <class T> inline void dump(T &v){irep(i, v){cout<<*i<<((i==--v.end())?'\n':' ');}}
inline string getline(){string s; getline(cin,s); return s;}
inline void yn(const bool b){b?fin("yes"):fin("no");}
inline void Yn(const bool b){b?fin("Yes"):fin("No");}
inline void YN(const bool b){b?fin("YES"):fin("NO");}
struct io{io(){ios::sync_with_stdio(false);cin.tie(0);}};
const int INF = INT_MAX;
constexpr ll LLINF = 1LL<<60;
constexpr ll MOD = 1000000007;
constexpr ld EPS = 1e-11;



int main() {
    
    int n;
    cin>>n;
    rep(i,1LL<<n){
        cout<<i<<":";
        rep(j,19){
            if(1LL<<j&i)cout<<" "<<j;
        }
        cout<<endl;
    }
}